This work develops a new multifidelity ensemble Kalman filter (MFEnKF) algorithm based on linear control variate framework. The approach allows for rigorous multifidelity extensions of the EnKF, where the uncertainty in coarser fidelities in the hierarchy of models represent control variates for the uncertainty in finer fidelities. Small ensembles of high fidelity model runs are complemented by larger ensembles of cheaper, lower fidelity runs, to obtain much improved analyses at only small additional computational costs. We investigate the use of reduced order models as coarse fidelity control variates in the MFEnKF, and provide analyses to quantify the improvements over the traditional ensemble Kalman filters. We apply these ideas to perform data assimilation with a quasi-geostrophic test problem, using direct numerical simulation and a corresponding POD-Galerkin reduced order model. Numerical results show that the two-fidelity MFEnKF provides better analyses than existing EnKF algorithms at comparable or reduced computational costs.

中文翻译：

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具有降阶控制变量的多保真集成卡尔曼滤波器

这项工作基于线性控制变量框架开发了一种新的多保真集成卡尔曼滤波器 (MFEnKF) 算法。该方法允许对 EnKF 进行严格的多保真扩展，其中模型层次结构中较粗略保真度的不确定性代表更精细保真度中不确定性的控制变量。高保真模型运行的小集合由更便宜的、低保真运行的更大集合补充，以仅以很小的额外计算成本获得大大改进的分析。我们研究了使用降阶模型作为 MFEnKF 中的粗略保真度控制变量，并提供分析以量化对传统集成卡尔曼滤波器的改进。我们应用这些想法来执行具有准地转测试问题的数据同化，使用直接数值模拟和相应的 POD-Galerkin 降阶模型。数值结果表明，双保真 MFEnKF 提供比现有 EnKF 算法更好的分析，但计算成本相当或降低。